How old is the generator? If less than 5, it's still under warranty.
replacing the entire pump housing may solve your problem. Many are plastic and if seals wear out, the shaft may not contact the drive gear at the back of the pump. replacement pump housing is fairly easy to replace. Hard to get at though. The pump housing with shaft, impeller and seals is about $120.00. Does the pump housing look like this ?
Replacement pump housing is made of bronze and much more durable.
Just remove the two allen head bolts at the top and bottom of the pump when you pull it out there is a drive gear on the back of the pump that you will need to remove and put on the new pump it is held on with a small allen screw use some locktite when you put it back together.
Manual is here